Some examples of research conducted in this project: In addition to studying the effects of external environment (chemical and biological) on human health, lately there has been considerable interest among researchers to study the effects of human internal microbial environment. Human body contains large diverse colonies bacteria and they may vary according by location on the body and by age of the person. For example, the composition of bacteria in an infant's gut changes from new born to a toddler. The data on the microbial composition are not the usual Euclidean space data but are constrained to sum to 1. Consequently standard statistical methods such as ANOVA or t-test are not applicable. In this research program we are developing novel statistical procedures for analyzing such complex data. Statistical methodologies are also being developed in this research project for analyzing data obtained from cell-cycle and circadian clock experiments. These new methods make use of the underlying geometry in the data. Researchers are routinely interested in performing statistical tests for comparing two or more experimental groups on the basis of high dimensional data (e.g. gene expression data) to identify variables (e.g. genes) that are deferentially expressed in each pair of groups. In this project we developed a novel powerful methodology for making such inferences while controlling overall false discoveries.